Thomas Tuchel was forced to line up without a recognised striker, and only six substitutes as the Premier League denied a request to have the game postponed.
Christian Pulisic was handed the reigns up front for Chelsea, but failed to make a dent on Wolves' defence, sparring with keeper Jose Sa late on, but to no avail.
The home side thought they had the lead inside the first 15 minutes when Daniel Podence tapped-in a Fernando Marcal cross, but an offside Raul Jimenez saw the goal ruled out.
There was more drama soon after when N'Golo Kante appeared to take down a ball forward with his hand, but the Frenchman was given a huge let-off by referee David Coote.
Chelsea attempted to turn the screw late on, but a combination of Pulisic's poor finishing and Mason Mount's lack of form saw their main goal-threats easily nullified.
Tuchel was less than happy that the game went ahead, in a weekend where six of the 10 Premier League fixtures were postponed due to COVID.
"It is very hard to understand it," Tuchel said.
"We applied to not play and put the situation under control and it was rejected,"
"We were made to be in the bus and travel together for three hours, were in meetings together, in dinner and lunch - and the situation does not feel like it will stop.
"We end up with players who play coming from injuries and we take the risk.
"I am worried from a medical point of view, we have had four days of consecutive positive tests. How will it stop if we are in a bus together and in meetings together?
"We are disappointed, we are a bit angry."
Tuchel confirmed seven members of his squad were out with positive Covid tests, but despite his protestations, his side now sit six points off of leaders Manchester City.